ellipticity \(\epsilon (<<1)\)  is defined as the ratio of the difference of the semimajor axis and the semiminor axis to their sum, and equals \(e^2/4\) , where \(e\)  is the eccentricity of the ellipse [1]}, [2]}.
Replacing \(n\)  with \(n^{\prime }\)  in Eq. 1, the perturbed scalar wave equation is
\((H+\epsilon \delta H)O_{l,m}^{\prime }(r,\theta )=\beta _{l,m}^{\prime 2}O_{l,m}^{\prime }(r,\theta ),\) 
